Absolute Value Graphs

Front

What is the definition of absolute value?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x|.

Front

What does the graph of an absolute value function look like?

Back

The graph of an absolute value function is a V-shape, opening upwards if the coefficient is positive and downwards if negative.

Front

What is the vertex of the absolute value function f(x) = |x| + 4?

Back

The vertex is the point (0, 4).

Front

How does the graph of f(x) = |x| + 4 differ from f(x) = |x|?

Back

f(x) = |x| + 4 is translated 4 units up from the graph of f(x) = |x|.

Front

What is the range of the function f(x) = |x| + 4?

Back

The range is y ≥ 4.

Front

What is the domain of the function f(x) = |x| + 4?

Back

The domain is all real numbers.

Front

What transformation does the equation y = |x + 4| + 7 represent?

Back

It represents a translation left 4 units and up 7 units.

Front

What is the equation of the absolute value function that opens downwards?

Back

An example is f(x) = -|x| + 4.

Front

How do you find the x-intercepts of the function f(x) = |x| - 4?

Back

Set f(x) = 0: |x| - 4 = 0, which gives x = 4 and x = -4.

Front

What is the effect of a negative coefficient in front of the absolute value function?

Back

It reflects the graph across the x-axis.